This evening I upgraded my xfce4 desktop to use
Linux 2.6.27-11-generic and the next time I rebooted my panels had completely disappeared.
The solution was to startup in terminal mode and run the following command:
$ mv ~/.config/xfce4 ~/.config/xfce4.backup
After another reboot, all is back to normal except for a couple small tweaks I have to make in order manually to restore my panels as they were.